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I find those two words a little confusing, so what are some contexts in which it's appropriate to use the word "incoherence/incoherent" rather than "inconsistency/inconsistent"?

Also, can the word "incoherence" be used like this "The Incoherence of X" to imply X not having a solid logical ground?

  • A person who's "incoherent" can't speak an intelligible sentence. A person who is "inconsistent" is a politician. – Hot Licks Nov 21 '15 at 23:20
  • If something is incoherent it makes no sense- it is a data stream that cannot be deciphered. If it's inconsistent the data stream can be deciphered but the data within it is erratic. – Jim Nov 21 '15 at 23:21
  • @Jim rather the data within it is contradictory. – deadrat Nov 22 '15 at 0:04
  • @deadrat- Well, contradictory data is one kind of inconsistency, but I would say that if the data represented a set of repeated measurements and instead of having a very small standard deviation, they varied greatly from measurement to measurement that would be inconsistent without being out-n-out contradictory. I suppose one could argue that if I measured the same distance twice and got 10'4" the first time and 8'7" the second time that might be more than just inconsistent, that would be contradictory. – Jim Nov 22 '15 at 0:13
  • The two words are quite synonyms. However, incoherence is related to a lack of logic and inconsistency refers to some specific contradiction. – Graffito Nov 22 '15 at 0:47
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The words do have somewhat overlapping meanings, and a quick dictionary search shows that the definitions tend to reference each other. But they tend to refer to different things and the connotations depend on context.

In general, inconsistent tends to refer to clear contradiction (often a specific contradiction) on some level, while incoherent can be a more general state of confusion.

For example, if measurements are inconsistent, that means some explicitly disagree with others (e.g., some are high, others are low). If measurements are incoherent, there is generally a greater level of confusion that does not permit a clear interpretation (e.g., the meter can't be read clearly to even determine the measurements).

When referring to logical proofs or philosophical systems, the implication is similar. A system which is logically inconsistent may not work in all cases, but the failure is likely to be a very specific point of contradiction. A system which is logically incoherent has more fundamental flaws which would perhaps cause the entire system to fall apart. Philosophers do, however, sometimes use the word incoherent to refer to a system with specific contradictions of logic (i.e., inconsistencies). Basically, I'd say inconsistent can refer to a specific flaw (an inconsistency), while there's no such thing as a single incoherency -- the system either passes and is coherent or fails completely and is incoherent.

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Incoherent implies that something is unintelligible - something that can not be understood, often due to confusion. It is mainly used to describe something said or written, as words can often be confusing or misunderstood. The drunk professor's incoherent ramblings were the first signs of his worsening condition.

Inconsistent describes something that does not follow a particular pattern. I am always late for work because the bus schedule is inconsistent.

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